Trigonometric equation (急) 20分

sinx + 3cosx - 2cosx - 1 = 0

(sinx + cosx) + 2cosx - 2cosx - 1 = 0

1 + 2cosx - 2cosx - 1 = 0 (Recall the identity sinx + cosx = 1)

2cosx - 2cosx = 0

cosx(cosx - 1) = 0

cosx = 0 or cosx = 1

x = 90* or 270* or x = 0* or 360* (For 0* <= x <= 360*)

Combined solution: x = 0*, 90*, 270* or 30*


2009-05-30 09:14:30 補充：
│cosx│ = sqrt3 / 2

cosx = sqrt3 / 2 or -sqrt3 / 2

x = 30* or 330* or x = 150* or 210*

Solution: x = 30*, 150*, 210* or 330*

2009-05-30 12:15:44 補充：
下面的朋友漏了一些solution

1. sin&sup2;x+3cos&sup2;x-2cosx-1=0
sin&sup2;x+cos&sup2;x+2cos&sup2;x-2cosx-1=0
1+2cos&sup2;x-2cosx-1=0
2cos&sup2;x=2cosx
cosx=0
x=90(degree)

2.︱ cosx︱= (開方3)/2
either cosx =(開方3)/2 or -cosx=(開方3)/2
x=30(degree) or x=330(degree)
if cosx is negative, then
x=150(degree) or x=210(degree)

︱ cosx︱= (開方3)/2
cosx=(開方3)/2 或 cosx=(-開方3)/2
x=30度,150度,210度或330度